Question

The charge per unit length of the four quadrant of the ring is 2λ,-2λ,λ and -λ respectively . the electric field at the centre is ​

Answer 1

Answer this question to simply

Answer 2

Answer:

The net electric Field at the centre is $\sqrt{2}\ \dfrac{k\lambda}{R}$

Explanation:

Let given charge i.e. $2\lambda, -2\lambda, \lambda, -\lambda$ per unit length is distributed on the quadrant of the circle in anticlockwise.

The direction of the electric field due to the charge density on the quadrant in first quadrant of the circle at the centre of is along the perpendicular bisector and away from it The magnitude is given by

$E_1=\dfrac{2k\lambda}{R}$

Similarly Electric field due other quadrants are

$E_2=\dfrac{2k\lambda}{R}\\E_3=\dfrac{k\lambda}{R}\\E_4=\dfrac{k\lambda}{R}$

so the direction of electric field due to  negative charge density is opposite to that of positive charge per unit length.

So adding all these by vector addition we get the net electric field at the centre is along the the diameter pointing in left direction of the the arrangement of the charges. The magnitude is given by

$E_{net}=\sqrt{2}\ \dfrac{k\lambda}{R}$